In our description of diffusio-osmosis, we consider a \(n\) -component fluid in contact with a solid surface, as shown in Fig. REF .
Initially, the only thermodynamic forces acting on the system are the chemical potential gradients of each species \(i\) , \(\mu _i\) .
The fluid can be divided into two regions: the bulk, where the fluid can be considered homogeneous, and the vicinity of the (solid-liquid) interface, where the concentration of the different species at a distance \(z\)  from the interface, \(c_i(z)\) , differs from its bulk value.
This deviation from the bulk concentrations decays as the distance from the surface is increased.
The reason why we first consider the expression for the entropy production is because it
contains both the thermodynamic driving forces and the conjugate fluxes [1]}.
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